Home educators from Action for Home Education have set about researching this issue of abuse in the HE community through Freedom of Information requests to local authorities. They have aggregated the results and have discovered that the rate of risk of abuse of HE children is actually, despite Mr Badman's stated claims to the contrary, under half the national rate.
Aside from huge question marks over Mr Badman's maths, a clear problem with his stated claims such as this one and this one is that he appears to conflate "being known to social care" or "being known to social services" with "being at risk of abusing a child".
It is unfortunately the case that a large number of perfectly well-functioning HE families are "known to social care" as a result of being spuriously referred, (often on account of the fact that the referrer doesn't realise that HE is a legal option). These families, despite the false referral, remain on SS records for the rest of time. "Known to social care" also refers to families who are in receipt of services, which would also bump up the numbers, given the high rate of children with special needs in the HE community. So if you exclude this lot, you return to the real numbers of HE children at risk of abuse, which is, yes, yet again - under half the national average. 
Mr Badman's recommendations would therefore appear to be based on false accounting and would represent a disproportionate and poorly targeted use of resources.
 Of course, it is possible that the Independent misquoted Mr. Badman. We note that he says in his Review of Home Education that:
8.12 "on the basis of local authority evidence and case studies presented, even acknowledging the variation between authorities, the number of children known to children’s social care in some local authorities is disproportionately high relative to the size of their home educating population."
However, it is easy to see how the Independent could have understood this statement to mean that these children were at risk of abuse, since Mr Badman seems to base a large number of his policy recommendations on just such a false interpretation.